A piece of a broken wheel is shown. It was taken to a machine shop to be replaced with a new “whole” wheel. Find the radius of the wheel AC=10cm, BD=3 cm and D is the midpoint of AC. Round to the nearest hundredth.
To find the radius of the whole wheel, we can use the geometric relationship between the radius and the diameter.
First, let's label the points in the diagram.
Let A and C be the endpoints of the piece of the broken wheel, with AC representing the arc. Let B be the endpoint of the broken piece of the wheel. Finally, let D be the midpoint of AC.
We know that BD is equal to 3 cm, and D is the midpoint of AC. This means that AD is equal to 3 cm and CD is also equal to 3 cm.
Now, let's consider the diameter of the whole wheel. The diameter is twice the radius. We can find the length of the diameter by adding the lengths of AD and CD.
Diameter of the whole wheel = AD + CD
Since AD and CD are both 3 cm, the diameter of the whole wheel is 3 cm + 3 cm = 6 cm.
Finally, to find the radius of the whole wheel, we need to divide the diameter by 2.
Radius of the whole wheel = Diameter of the whole wheel / 2
Radius of the whole wheel = 6 cm / 2 = 3 cm
Therefore, the radius of the whole wheel is 3 cm.